Preheat oven to 350 degrees. Grease a 13x9 inch baking pan.
Arrange chicken in single layer in prepared baking pan.
Combine 1 1/2 cups of milk, the flour, eggs and salt in a medium bowl. Beat at high speed until well blended. Add oil and tarragon to egg mixture and mix well. Pour over chicken in baking pan.
Bake until an instant-read thermometer inserted in center of meat registers 180 degrees, about 65 minutes.
Drain mushrooms. Heat the butter in a small saucepan until melted. Stir in the mushrooms. Cook, stirring frequently, until heated through.
Add remaining milk and soup and mix well. Cook,stirring continually, until heated through and of sauce consistency. Serve with chicken. You can also stir in a 1/2 cup of green peas in the mushroom sauce. Garnish with a little paprika.